It has been found from past experience that of the articles produced by a factory, 20% come from machine 1, 30% come from machine 2 and 50% come from machine 3. The percentages of satisfactory articles among those produced are 95% for machine 1, 85% for machine 2 and 90% for machine 3.
(a) An article is chosen at random from a lot. What is the probability that it is satisfactory ?
(b) Assuming that it is satisfactory, what is the probability that it was produced by machine 1 ?